Table 7 Statistical results HV of the mathematical test functions: ZDT and CEC2009 functions.
function | HV | MALO | MSSA | MOPSO | MOSCA | MOSCHO |
|---|---|---|---|---|---|---|
ZDT1 | Av | 0.7376 | 0.6655 | 0.9358 | 0.9996 | 0.9998 |
SD | 0.0251 | 0.0157 | 0.0185 | 0.0005 | 4.8795e-05 | |
WRT | - | - | - | - | ||
ZDT3 | Av | 0.7122 | 0.6544 | 0.8912 | 0.9970 | 0.9970 |
SD | 0.0178 | 0.0285 | 0.0271 | 0.0050 | 0.0093 | |
WRT | - | - | - | - | ||
ZDT4 | Av | 0.8341 | 0.8751 | 0.8798 | 0.9263 | 1 |
SD | 0.0396 | 0.0187 | 0.0516 | 0.0927 | 0 | |
WRT | + | + | - | + | ||
UF1 | Av | 0.9973 | 0.9972 | 0.9998 | 0.9997 | 0.9998 |
SD | 0.0014 | 0.0026 | 3.5186e-05 | 0.0001 | 4.1403e-05 | |
WRT | - | - | - | - | ||
UF2 | Av | 0.9831 | 0.9858 | 0.9884 | 0.9994 | 0.9995 |
SD | 0.0078 | 0.0068 | 0.0108 | 0.0001 | 0.0001 | |
WRT | - | - | + | - | ||
UF3 | Av | 0.9873 | 0.9930 | 1.0004 | 1.0004 | 1.0003 |
SD | 0.0062 | 0.0073 | 0.0002 | 0.0001 | 0.0002 | |
WRT | - | - | - | - | ||
UF4 | Av | 0.9960 | 0.9985 | 0.99983 | 0.9996 | 0.99984 |
SD | 0.0020 | 0.0016 | 0.0001 | 0.0001 | 5.0709e-05 | |
WRT | - | - | - | - | ||
UF5 | Av | 0.9894 | 0.9921 | 0.9972 | 0.9971 | 0.9971 |
SD | 0.0032 | 0.0041 | 0.0002 | 0.0004 | 0.0002 | |
WRT | - | - | - | - | ||
UF6 | Av | 0.9963 | 0.9988 | 0.9991 | 0.9987 | 0.9994 |
SD | 0.0022 | 0.0009 | 0.0006 | 0.0011 | 0.0005 | |
WRT | - | - | + | - | ||
UF7 | Av | 0.9897 | 0.9746 | 0.9999 | 0.9883 | 0.9993 |
SD | 0.0082 | 0.0062 | 3.5186e-05 | 0.0089 | 0.0002 | |
WRT | - | - | + | - | ||
For WRT | +/-/= | 1/9/0 | 1/9/0 | 3/7/0 | 1/9/0 |
